| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then find median/quartiles from cumulative frequency |
| Difficulty | Moderate -0.8 This is a straightforward application of standard histogram construction with unequal class widths and median estimation from grouped data. Both techniques are routine S1 skills requiring only direct application of formulas (frequency density for histogram, linear interpolation for median) with no problem-solving or conceptual challenges beyond basic procedural competence. |
| Spec | 2.02b Histogram: area represents frequency |
| Distance \(( d\) miles \()\) | \(0 \leqslant d < 50\) | \(50 \leqslant d < 100\) | \(100 \leqslant d < 200\) | \(200 \leqslant d < 400\) |
| Frequency | 360 | 400 | 307 | 133 |
| Answer | Marks | Guidance |
|---|---|---|
| Distance | fr | width |
| 0– | 0 | 50 |
| 50– | 0 | 50 |
| 100– | 7 | 100 |
| 200–400 | 133 | 200 |
| M1 for fds; A1 CAO | Accept any suitable unit for fd such as freq per 50 miles | L1 linear scales on both axes and label; W1 width of bars; H1 height of bars |
| Answer | Marks | Guidance |
|---|---|---|
| Median \(= 600\text{th}\) distance | B1 for \(600^{\text{th}}\) | |
| \(\text{Estimate} = 50 + \frac{240}{400}\times50 = 50 + 30 = 80\) | M1 for attempt to interpolate; A1 CAO | [3 marks] |
# Question 4:
## Part (i)
| Distance | fr | width | f dens |
|---|---|---|---|
| 0– | 0 | 50 | 7.200 |
| 50– | 0 | 50 | 8.000 |
| 100– | 7 | 100 | 3.070 |
| 200–400 | 133 | 200 | 0.665 |
M1 for fds; A1 CAO | Accept any suitable unit for fd such as freq per 50 miles | L1 linear scales on both axes and label; W1 width of bars; H1 height of bars | **[5 marks]**
## Part (ii)
Median $= 600\text{th}$ distance | B1 for $600^{\text{th}}$ |
$\text{Estimate} = 50 + \frac{240}{400}\times50 = 50 + 30 = 80$ | M1 for attempt to interpolate; A1 CAO | **[3 marks]**4 The frequency table below shows the distance travelled by 1200 visitors to a particular UK tourist destination in August 2008.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\hline
Distance $( d$ miles $)$ & $0 \leqslant d < 50$ & $50 \leqslant d < 100$ & $100 \leqslant d < 200$ & $200 \leqslant d < 400$ \\
\hline
Frequency & 360 & 400 & 307 & 133 \\
\hline
\end{tabular}
\end{center}
(i) Draw a histogram on graph paper to illustrate these data.\\
(ii) Calculate an estimate of the median distance.
\hfill \mbox{\textit{OCR MEI S1 Q4 [8]}}